Superconductivity in spinel-type compounds ${\mathrm{CuRh}}_2$${\mathrm{S}}_4$ and ${\mathrm{CuRh}}_2$${\mathrm{Se}}_4$

An extensive study of electrical resistivity, ac magnetic susceptibility, magnetization, specific heat, and NMR has been made on high purity samples of the spinel compounds ${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$ and ${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$. The superconducting transitions occur at 4.70 K in ${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$ and 3.48 K in ${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$. The magnetic susceptibilities show perfect diamagnetism in both compounds. Upper critical fields at T=0 are estimated to be 20.0 and 4.40 kOe, the lower critical fields at T=0 are 70 and 95 Oe, respectively. The thermodynamic critical fields at T=0 are 704 Oe (${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$) and 445 Oe (${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$). These values are obtained from the temperature dependence of the free energy. These compounds are type-II superconductors with Ginzburg-Landau parameters κ=21 (${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$) and κ=6.6 (${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$) at T=0. The electron-phonon coupling constants, ${\lambda }_{\mathrm{ep}}$=0.68 (${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$) and ${\lambda }_{\mathrm{ep}}$=0.64 (${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$), are obtained using the McMillan formula. The copper nuclear-spin-relaxation rate as a function of temperature shows a pronounced coherence peak just below ${\mathit{T}}_{\mathit{c}}$ for ${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$. Experimental results are analyzed on the basis of the BCS theory. These compounds exist between weak- and intermediate-coupling superconductors which are driven by electron-phonon interaction. The Debye temperatures FTHETA of these materials are 230 K (${\mathrm{CuRh}}_2$ ${\mathrm{S}}_4$) and 211 K (${\mathrm{CuRh}}_2$ ${\mathrm{Se}}_4$).